Question 1:
1) The marketing director of a small chain of specialty coffee/pastry "cafés" collected data on 120 customers at random (offering a free cup of coffee if the customer filled out the questionnaire) in a study to determine whether satisfaction with various attributes of the café (e.g., quality of service) (Y) is related to various demographics of the customer (X). The data considering quality of service (a value ranging from 0-4, by tenths and the demographic, AGE (in years), are in the Excel file named "sat vs. age". (e.g., first responder: AGE=21, SAT=3.9)
a) Obtain the Least Squares line.
b) Obtain a point estimate of the mean satisfaction for customers with age = 30.
c) What is the point estimate of the change in satisfaction when age increases by one year?
Question 2:
Refer to the "sat. vs. age" data of "Question 1".
a) Obtain a 95% confidence interval for the mean satisfaction for customers age 28. Interpret your interval.
b) Mary Jones is 28 years old. Predict her satisfaction and find a 95% confidence interval for this value.
c) Is the interval in part b) wider than that of part a)? Should it be?
d) Run an F-test to test Ho: B = 0 vs. H1: B≠0 with a = .01. What is your conclusion in practical terms?
Question 3:
The data in Excel file named "Advertising Recall" represent the number of ads for a product recalled (Y) over time (X). There were 900 people in the study, divided into 9 sets of 100. Each set of 100 people were polled after a certain number of days, three groups after 1 day, three groups after 3 days, three groups after 5 days, three groups after 7 days, and 3 groups after 9 days. The Y values are the average number of ads for the product recalled (e.g., first data value, Y = .07, X = 9).
a) Fit a OLS line to the data.
b) Perform the F-test to determine whether or not there is a lack of fit to a linear regression function. Use a = .05.
ADVERTISING RECALL
Question 4:
The data in the Excel file, "Brand Awareness" represent the relationship between a "brand awareness measure"* (Y) and age (X) for 8 children. (e.g., value 1: Y = 63, X = 5)
a) Obtain the OLS regression line.
b) Examine the standardized residuals. What is suggested about data point 7?
c) mit case 7 from the data and then obtain the OLS regression line.
d) Using the regression results from part c), find a 99% confidence interval for the Y observation when X = 12.
e) Does the Y value for case 7 fall inside or outside of this interval? What does this suggest?
*A complex measure using a large multi-item scale